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No.8 Toby Faletau’s well-worked score gave Wales a 16-10 lead in the second half before replacement Francois Hougaard's try and Morne Steyn's conversion gave South Africa a barely-deserved victory.
However Wales did have chances to regain the lead as Rhys Priestland off target with a drop goal in front of the posts and James Hook hooking a kickable penalty late on.
Gatland also believe a first-half Hook penalty snuck between the posts even though it was not awarded by the officials and the Kiwi coach maintains that proves how fine the margins are at the very top of the international game.
He said: “I'm very proud of the effort the players put in. We did everything but win the game. It is about taking your opportunities.
“We didn't start well and held off them in those first couple of minutes. But after [that] we dominated territory and possession and played some great rugby.
“We put ourselves in with a chance to win but in the end we weren't quite good enough.
“The players will be devastated but we had a chance - a [Rhys Priestland] drop-goal in front of the posts, [James] Hooky had a penalty.
“But we got a bonus point out of it and we will take a massive amount from it. I thought we might have had a penalty in the first half and Frans Steyn said in the tunnel at half-time he thought it had gone over.
“But that's what competing at the highest level is all about.
“When you get those chances in front of their posts you have got to put them through.
“It's just that little half a per cent we've got to learn from.
“We have been knocking on the door for a while and if we get over that hurdle it will be good for us for the rest of the tournament.”
Wales made the worst possible start when Morne Steyn set up full-back Francois Steyn for the game’s opening try inside the first three minutes.
Another Morne Steyn penalty put the champions 10-0 to the good but two Hook penalties meant they only had a four-point advantage at the break.
That was wiped out entirely when Jamie Roberts – the British & Irish Lions’ player of the series against the Boks in 2009 – made a strong charge which allowed Faletau to crash over for a converted score.
But South Africa responded when Hougaard drifted through a huge gap in the Wales defence for a converted try and neither Priestland nor Hook could make themselves a hero.